Question

The number of subsets of a set of order three is
a) $ 3 $
b) $ 6 $
c) $ 8 $
d) $ 9 $

Answer 1

Hint: The number of subsets for a set containing ‘n’ number of elements is given by the formula $ {2^n} $ . For example consider the set $ A = \left\{ {a,b,c,d,e} \right\} $ , this set contains five elements so the total number of subsets would be $ {2^5} $ which is equal to $ 32 $

Complete step-by-step answer:
Given to us that the order of a set is three i.e. the number of elements in the set is three.
We are asked to find the number of subsets for this set.
In order to find this, we apply the formula, total number of subsets for a set containing ‘n’ elements is $ {2^n} $
In the question given to us, the value of ‘n’ is two.
So the number of subsets for a set with three elements will be $ {2^3} $ which by solving, we get $ 8 $
Therefore the total numbers of subsets for the given set with order three is eight.
Therefore the total number of subsets for a set containing three elements are $ eight $ i.e. option c.
So, the correct answer is “Option C”.

Note: We can also explain this by taking an example of a set with three elements as $ S = \left\{ {1,2,3} \right\} $
To write the subsets of this set, we start with subsets of single order: $ \left\{ 1 \right\},\left\{ 2 \right\},\left\{ 3 \right\} $
Subsets of order two: $ \left\{ {1,2} \right\},\left\{ {2,3} \right\},\left\{ {1,3} \right\} $
We know that every set is a subset of itself and also null set is a subset of every set so the rest of the subsets are $ \left\{ {1,2,3} \right\},\left\{ \emptyset \right\} $
By adding all the subsets we get eight. Therefore the total number of subsets would be eight.